Information diffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, disease contagion between individuals, cascading failures in power grids. During the diffusion, some network structures play critical roles and primarily affect network structure and functions. For example, in social networks, one can spread messages in the network quickly through the critical nodes [1]}; in epidemic networks, one may reduce the diffusion of epidemic with controlling influential nodes [2]}. Therefore, identifying critical (influential) nodes and edges has practical importance in network science. There are many studies in the literature for the critical node detection problem in networks. Typical methods are based on network topology. Some studies use nodes' degree, such as degree centrality [3]} and H-index [4]}, some use paths in networks, such as closeness centrality [5]} and betweenness centrality [6]}, and some use eigendecomposition of graphs, such as PageRank [7]} and DFF centrality [8]}. In addition, some researchers use node deletion or contraction to distinguish the importance of nodes [9]}, [10]}.
